Answer :
To find the expression for [tex]\((4x^4 + 2x^2 - 6)\)[/tex] subtracted by [tex]\((3x^4 + 2x^2 - 6)\)[/tex], follow these steps:
1. Start with the two given polynomials:
[tex]\[
\text{First polynomial: } 4x^4 + 2x^2 - 6
\][/tex]
[tex]\[
\text{Second polynomial: } 3x^4 + 2x^2 - 6
\][/tex]
2. To perform the subtraction, subtract each corresponding term of the second polynomial from the first polynomial:
[tex]\[
(4x^4 + 2x^2 - 6) - (3x^4 + 2x^2 - 6)
\][/tex]
3. Distribute the negative sign across the second polynomial:
[tex]\[
(4x^4 + 2x^2 - 6) - 3x^4 - 2x^2 + 6
\][/tex]
4. Combine like terms:
[tex]\[
4x^4 - 3x^4 + 2x^2 - 2x^2 - 6 + 6
\][/tex]
5. Simplify each group of like terms:
[tex]\[
\text{Combine } 4x^4 \text{ and } -3x^4: \quad 4x^4 - 3x^4 = x^4
\][/tex]
[tex]\[
\text{Combine } 2x^2 \text{ and } -2x^2: \quad 2x^2 - 2x^2 = 0
\][/tex]
[tex]\[
\text{Combine } -6 \text{ and } 6: \quad -6 + 6 = 0
\][/tex]
6. The resulting polynomial is:
[tex]\[
x^4 + 0 + 0 = x^4
\][/tex]
So, the polynomial [tex]\((3x^4 + 2x^2 - 6)\)[/tex] subtracted from [tex]\((4x^4 + 2x^2 - 6)\)[/tex] is [tex]\(\boxed{x^4}\)[/tex]. Thus, the correct answer is:
A) [tex]\(x^4\)[/tex]
1. Start with the two given polynomials:
[tex]\[
\text{First polynomial: } 4x^4 + 2x^2 - 6
\][/tex]
[tex]\[
\text{Second polynomial: } 3x^4 + 2x^2 - 6
\][/tex]
2. To perform the subtraction, subtract each corresponding term of the second polynomial from the first polynomial:
[tex]\[
(4x^4 + 2x^2 - 6) - (3x^4 + 2x^2 - 6)
\][/tex]
3. Distribute the negative sign across the second polynomial:
[tex]\[
(4x^4 + 2x^2 - 6) - 3x^4 - 2x^2 + 6
\][/tex]
4. Combine like terms:
[tex]\[
4x^4 - 3x^4 + 2x^2 - 2x^2 - 6 + 6
\][/tex]
5. Simplify each group of like terms:
[tex]\[
\text{Combine } 4x^4 \text{ and } -3x^4: \quad 4x^4 - 3x^4 = x^4
\][/tex]
[tex]\[
\text{Combine } 2x^2 \text{ and } -2x^2: \quad 2x^2 - 2x^2 = 0
\][/tex]
[tex]\[
\text{Combine } -6 \text{ and } 6: \quad -6 + 6 = 0
\][/tex]
6. The resulting polynomial is:
[tex]\[
x^4 + 0 + 0 = x^4
\][/tex]
So, the polynomial [tex]\((3x^4 + 2x^2 - 6)\)[/tex] subtracted from [tex]\((4x^4 + 2x^2 - 6)\)[/tex] is [tex]\(\boxed{x^4}\)[/tex]. Thus, the correct answer is:
A) [tex]\(x^4\)[/tex]
